Throughout the progression of early forms of Christianity, travel, trade and exploration were intensifying with ardency in the search for a better life on earth, meaning that Christians were meeting new peoples and encountering new ideas. With the Crusades – ‘a seismic culture shock’ (Bernstein, 1998:19) of the collision of westerners with an Arab empire – propelled developments further as a result of the combination of the Christians’ faith in the future and the Arabs’ knowledge of the Hindu numbering system that had been developing parallel to that of the Greeks.
For Bernstein, ‘the story of numbers begins in 1202’ (1998:23) when Fibonacci, following and encounter with an Arab mathematician astute in the Hindu-Arabic numbering system, was inspired to write of their benefits in his book Liber Abaci. This book drew attention to the revolutionary way in which numbers could be substituted for the Hebrew, Greek and Roman systems there were currently in place that used letter for counting and calculating.
It exhibited a high level of sophistication featuring ‘calculations using whole numbers and fractions, rules of proportion, extraction of square roots and roots of higher orders, and even solutions for linear and quadratic equations’ (1998:24). A fundamental benefit of the Hindu-Arabic numbering system was the invention of zero. According to Bernstein this revolutionised the old numbering system in two ways:
‘First, it meant that people could use only ten digits, from zero to nine, to perform every conceivable calculation and to write any conceivable number. Second, it meant that a sequence of numbers like 1, 10, 100 would indicate that the next number in the sequence would be 1000. Zero makes the whole structure of the numbering system immediately visible and clear. ‘ (Bernstein, 1998:33) Furthermore, of particular advancement was the method of practical application that Fibonacci used. Bernstein provides the example that:
‘he described and illustrated many innovations that the new numbers made possible in commercial bookkeeping, such as figuring profit margins, money-changing, conversions of weights and measures, and – though usury was still prohibited in many places – he even included calculations of interest payments. ‘ (Bernstein 1998:25) This use of the new numbering system in conjunction with practical application was the first step towards making measurement ‘the key factor in the taming of risk.
But society was not yet prepared to attach numbers to risk’ (1998:28). The next significant development in this respect came with the early Renaissance period which was to become a momentous time of discovery in both art and science, originating in Italy. With the publication of a book entitled Summa de arithmetic, geometria et proportionalita by the Franciscan monk Luca Paccioli, came the most extensive discussion of double-entry bookkeeping to date.
Furthermore, his inclusion of a puzzle with the underlying core question ‘how do we divide the stakes in an uncompleted game’ prompted heated debates, and the resolution ‘marked the beginning of a systematic analysis of probability – the measure of our confidence that something is going to happen. It brings us to the threshold of the quantification of risk’ (Bernstein, 1998:43). The early Renaissance period was marked with developments with regard to risk and probability and another significant transpiration came with the work of Cardano, a sixteenth century physician, entitled Liber de Ludo Aleae.
Herein he defined, ‘for the first time, what is now the conventional format for expressing probability as a fraction: the number of favourable outcomes divided by the “circuit” – that is, the total number of possible outcomes’ (Bernstein, 1998:50). According to Bernstein this book was the first known attempt to ‘put measurement at the service of risk’ and that it was ‘through this process… that risk management evolved’ (1998:54). With the maturity of the Renaissance and the dawn of modernity that it brought about, the interdependent systems of capitalism and industrialism propelled notions of risk and probability forward.
‘But capitalism could not have flourished without two new activities that had been unnecessary so long as the future was a matter of chance or of God’s will. The first was bookkeeping, a humble activity but one that encouraged the dissemination of the new techniques of numbering and counting. The other was forecasting, a much less humble and far more challenging activity that links risk-taking with direct payoffs’. (Bernstein 1998:21)
From the seventeenth century the final stage of the Enlightenment period encompassed a strive to find the key to human progress and order, expressed by Lupton as ‘objective knowledge of the world through scientific exploration and rational thinking’ (1999:6). Interest in the subject of risk and probability spread through France and onto Switzerland, Germany and England, and the eighteenth century was characterised by advances in calculus and algebra which ‘led to increasingly abstract concepts that provided the foundation for many practical applications of probability’ (Bernstein 1998:55), predominantly those of insurance and investment.
Prior to this juncture it is difficult to understand why the concept of risk and the strengthening notion of probability were not incorporated into society. After all the above evidence proves that all the essential components were in play, albeit in a primitive form. Bernstein attempts to retort through his explanation that societies preceding the Renaissance perceived the future as: ‘little more than a matter of luck or the result of random variations, and most of their decisions were driven by instinct.
When the conditions of life are so closely linked to nature, not much is left to human control’ (Bernstein, 1998:18). Lupton also maintains that although the notion of risk ‘first appeared in the Middle Ages, related to maritime insurance’, it did not yet resemble any form that we recognise today in that it ‘excluded the idea of human fault and responsibility’ (Lupton, 1999:5). More specifically it is argued that each breakthrough, no matter how seemingly minor, played a vital part in the development of probability theory and risk management, without which it would never have been possible.
The Arabs for example were unable to advance due to their belief in the determining forces of the Gods over our future, despite their already advanced mathematical ideas. For Covello and Mumpower, the rapid development of probability theory in the seventeenth and eighteenth centuries could ‘be traced to the rise of capitalism and to the desire of the new mercantile class for improved methods of business calculation and for greater economic security in the form of insurance’.
